### Abstract

The Optical Multi-Trees (OMULT) is an interconnection network proposed by Sinha and Bandyopadhyay [B.P. Sinha, S. Bandyopadhyay, OMULT: An optical interconnection system for parallel computing, Lecture notes in Computer Science 3149 (2004) 302-312], for optoelectronic parallel computers. Various algorithms including matrix multiplication, DFT computation, sorting, prefix sum have been successfully mapped on this architecture. In this paper, we develop efficient parallel algorithms for some commonly used permutations namely, bit reversal, vector reversal, perfect shuffle, unshuffle and transpose on the OMULT network. Our algorithm for bit reversal permutation requires 8 log n electronic moves +7 optical moves for n^{2} data elements and O (n) electronic moves +3 optical moves for n^{3} data elements; the vector reversal for n^{3} data elements requires 3 g (n) electronic moves +4 optical moves, where g (n) is the time for local vector reversal on n data elements; the perfect shuffle for n^{3} data elements requires (3 f (n) + 8) electronic moves +8 optical moves, where f (n) is the time for local perfect shuffle on n data elements, and the transpose for n^{3} data elements runs in at most three optical moves, all using 2 n^{3}-n^{2} processors.

Original language | English |
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Pages (from-to) | 2656-2665 |

Number of pages | 10 |

Journal | Computers and Mathematics with Applications |

Volume | 56 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1 Nov 2008 |

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### Keywords

- Bit reversal
- Optical multi-trees
- Optoelectronic computer
- Permutation routing
- Shuffle
- Transpose
- Vector reversal

### ASJC Scopus subject areas

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*56*(10), 2656-2665. https://doi.org/10.1016/j.camwa.2008.03.060